Progression in multiplication and division - new curriculum



Progression: Multiplication and Division

Programme of study (statutory requirements)

|Y1 |Y2 |Y3 |Y4 |Y5 |Y6 |

|Multiplication and division|Multiplication and division |Multiplication and division |Multiplication and division |Multiplication and division |Addition, subtraction, multiplication |

| | | | | |and division |

| |Pupils should be taught to: |Pupils should be taught to: |Pupils should be taught to: |Pupils should be taught to: | |

|Pupils should be taught to:|recall and use multiplication and | | | |Pupils should be taught to: |

| |division facts for the 2, 5 and 10 |recall and use multiplication and |recall multiplication and division facts|identify multiples and factors, including | |

| |multiplication tables, including |division facts for the 3, 4 and 8 |for multiplication tables up to 12 × 12 |finding all factor pairs of a number, and |multiply multi-digit numbers up to 4 |

|solve one-step problems |recognising odd and even numbers |multiplication tables | |common factors of two numbers |digits by a two-digit whole number |

|involving multiplication | | |use place value, known and derived facts|know and use the vocabulary of prime numbers, |using the formal written method of long|

|and division, by |calculate mathematical statements for |write and calculate mathematical |to multiply and divide mentally, |prime factors and composite (non-prime) numbers|multiplication |

|calculating the answer |multiplication and division within the |statements for multiplication and |including: multiplying by 0 and 1; | |divide numbers up to 4 digits by a |

|using concrete objects, |multiplication tables and write them |division using the multiplication |dividing by 1; multiplying together |establish whether a number up to 100 is prime |two-digit whole number using the formal|

|pictorial representations |using the multiplication (×), division |tables that they know, including for |three numbers |and recall prime numbers up to 19 |written method of long division, and |

|and arrays with the support|(÷) and equals (=) signs |two-digit numbers times one-digit | |multiply numbers up to 4 digits by a one- or |interpret remainders as whole number |

|of the teacher | |numbers, using mental and progressing |recognise and use factor pairs and |two-digit number using a formal written method,|remainders, fractions, or by rounding, |

| |show that multiplication of two numbers|to formal written methods |commutativity in mental calculations |including long multiplication for two-digit |as appropriate for the context |

| |can be done in any order (commutative) | | |numbers |divide numbers up to 4 digits by a |

| |and division of one number by another |solve problems, including missing |multiply two-digit and three-digit |multiply and divide numbers mentally drawing |two-digit number using the formal |

| |cannot |number problems, involving |numbers by a one-digit number using |upon known facts |written method of short division where |

| | |multiplication and division, including |formal written layout |divide numbers up to 4 digits by a one-digit |appropriate, interpreting remainders |

| |solve problems involving multiplication|positive integer scaling problems and | |number using the formal written method of short|according to the context |

| |and division, using materials, arrays, |correspondence problems in which n |solve problems involving multiplying and|division and interpret remainders appropriately|perform mental calculations, including |

| |repeated addition, mental methods, and |objects are connected to m objects |adding, including using the distributive|for the context |with mixed operations and large numbers|

| |multiplication and division facts, | |law to multiply two digit numbers by one|multiply and divide whole numbers and those |identify common factors, common |

| |including problems in contexts | |digit, integer scaling problems and |involving decimals by 10, 100 and 1000 |multiples and prime numbers |

| | | |harder correspondence problems such as n|recognise and use square numbers and cube |use their knowledge of the order of |

| | | |objects are connected to m objects |numbers, and the notation for squared (2) and |operations to carry out calculations |

| | | | |cubed (3) |involving the four operations |

| | | | |solve problems involving multiplication and |solve addition and subtraction |

| | | | |division including using their knowledge of |multi-step problems in contexts, |

| | | | |factors and multiples, squares and cubes |deciding which operations and methods |

| | | | |solve problems involving addition, subtraction,|to use and why |

| | | | |multiplication and division and a combination |solve problems involving addition, |

| | | | |of these, including understanding the meaning |subtraction, multiplication and |

| | | | |of the equals sign |division |

| | | | |solve problems involving multiplication and |use estimation to check answers to |

| | | | |division, including scaling by simple fractions|calculations and determine, in the |

| | | | |and problems involving simple rates |context of a problem, an appropriate |

| | | | | |degree of accuracy |

Notes and guidance (non-statutory)

|Y1 |Y2 |Y3 |Y4 |Y5 |Y6 |

|Multiplication and division|Multiplication and division |Multiplication and division |Multiplication and division |Multiplication and division |Addition, subtraction, multiplication |

| | | | | |and division |

| |Pupils use a variety of language to |Pupils continue to practise their |Pupils continue to practise recalling |Pupils practise and extend their use of the | |

|Through grouping and |describe multiplication and division. |mental recall of multiplication tables |and using multiplication tables and |formal written methods of short multiplication |Pupils practise addition, subtraction, |

|sharing small quantities, | |when they are calculating mathematical |related division facts to aid fluency. |and short division (see Mathematics Appendix |multiplication and division for larger |

|pupils begin to understand:|Pupils are introduced to the |statements in order to improve fluency.| |1). They apply all the multiplication tables |numbers, using the formal written |

|multiplication and |multiplication tables. They practise to|Through doubling, they connect the 2, 4|Pupils practise mental methods and |and related division facts frequently, commit |methods of columnar addition and |

|division; doubling numbers |become fluent in the 2, 5 and 10 |and 8 multiplication tables. |extend this to three-digit numbers to |them to memory and use them confidently to make|subtraction, short and long |

|and quantities; and finding|multiplication tables and connect them | |derive facts (for example 600 ÷ 3 = 200 |larger calculations. |multiplication, and short and long |

|simple fractions of |to each other. They connect the 10 |Pupils develop efficient mental |can be derived from 2 x 3 = 6). | |division (see Mathematics Appendix 1). |

|objects, numbers and |multiplication table to place value, |methods, for example, using | |They use and understand the terms factor, | |

|quantities. |and the 5 multiplication table to the |commutativity and associativity (for |Pupils practise to become fluent in the |multiple and prime, square and cube numbers. |They undertake mental calculations with|

| |divisions on the clock face. They begin|example, 4 × 12 × 5 = 4 × 5 × 12 = 20 ×|formal written method of short |Pupils interpret non-integer answers to |increasingly large numbers and more |

|They make connections |to use other multiplication tables and |12 = 240) and multiplication and |multiplication and short division with |division by expressing results in different |complex calculations. |

|between arrays, number |recall multiplication facts, including |division facts (for example, using 3 × |exact answers (see Mathematics Appendix |ways according to the context, including with | |

|patterns, and counting in |using related division facts to perform|2 = 6, 6 ÷ 3 = 2 and 2 = 6 ÷ 3) to |1). |remainders, as fractions, as decimals or by |Pupils continue to use all the |

|twos, fives and tens. |written and mental calculations. |derive related facts (30 × 2 = 60, 60 ÷| |rounding (for example, 98 ÷ 4 = 98/4 = 24 r 2 =|multiplication tables to calculate |

| | |3 = 20 and 20 = 60 ÷ 3). |Pupils write statements about the |241/2 = 24.5 ≈ 25). |mathematical statements in order to |

| |Pupils work with a range of materials | |equality of expressions (for example, | |maintain their fluency. |

| |and contexts in which multiplication |Pupils develop reliable written methods|use the distributive law 39 × 7 = 30 × 7|Pupils use multiplication and division as | |

| |and division relate to grouping and |for multiplication and division, |+ 9 × 7 and associative law (2 × 3) × 4 |inverses to support the introduction of ratio |Pupils round answers to a specified |

| |sharing discrete and continuous |starting with calculations of two-digit|= 2 × (3 × 4)). They combine their |in year 6, for example, by multiplying and |degree of accuracy, for example, to the|

| |quantities, to arrays and to repeated |numbers by one-digit numbers and |knowledge of number facts and rules of |dividing by powers of 10 in scale drawings or |nearest 10, 20, 50 etc, but not to a |

| |addition. They begin to relate these to|progressing to the formal written |arithmetic to solve mental and written |by multiplying and dividing by powers of a 1000|specified number of significant |

| |fractions and measures (for example, 40|methods of short multiplication and |calculations for example, 2 x 6 x 5 = 10|in converting between units such as kilometres |figures. |

| |÷ 2 = 20, 20 is a half of 40). They use|division. |x 6 = 60. |and metres. | |

| |commutativity and inverse relations to | | | |Pupils explore the order of operations |

| |develop multiplicative reasoning (for |Pupils solve simple problems in |Pupils solve two-step problems in |Distributivity can be expressed as a(b + c) = |using brackets; for example, 2 + 1 x 3 |

| |example, 4 × 5 = 20 and 20 ÷ 5 = 4). |contexts, deciding which of the four |contexts, choosing the appropriate |ab + ac. |= 5 and (2 + 1) x 3 = 9. |

| | |operations to use and why. These |operation, working with increasingly | | |

| | |include measuring and scaling contexts,|harder numbers. This should include |They understand the terms factor, multiple and |Common factors can be related to |

| | |(for example, four times as high, eight|correspondence questions such as the |prime, square and cube numbers and use them to |finding equivalent fractions. |

| | |times as long etc.) and correspondence |numbers of choices of a meal on a menu, |construct equivalence statements (for example, | |

| | |problems in which m objects are |or three cakes shared equally between 10|4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 =| |

| | |connected to n objects (for example, 3 |children. |92 x 10). | |

| | |hats and 4 coats, how many different | | | |

| | |outfits?; 12 sweets shared equally | |Pupils use and explain the equals sign to | |

| | |between 4 children; 4 cakes shared | |indicate equivalence, including in missing | |

| | |equally between 8 children). | |number problems (for example, 13 + 24 = 12 + | |

| | | | |25; 33 = 5 x □). | |

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Herts for Learning – Teaching and Learning

Herts for Learning – Teaching and Learning

Herts for Learning – Teaching and Learning

Herts for Learning – Teaching and Learning

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